QR questions

[kov82]

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Hi guys, I'm struggling with these word problems if someone can show a simple/quick way to do them, for those who took the test, were these the type of problems you saw on the real thing?


In May of 1965, a father's age was three times the sum
of the ages of his two sons. In May of 1975, the
father's age was 10 years greater than the sum of his
sons' ages. If the difference between the sons' ages is
four years, how much older is the father than his older
son?
A. 23 years answer
B. 13 years
C. 33 years
D. 27 years
E. 40 years


A dining room table is selling at a 20% discount,
which is $120 more than 1/2 the list price. What is the
list price of the table?
A. $240
B. $400 answer
C. $200
D. $360
E. $300



It takes 6 workers 6 weeks to lay 1000 feet of pipe.
How long will it take 8 workers to lay 400 yards of
pipe?
A. 5.4 weeks answer
B. 3.75 weeks
C. 3.2 weeks
D. 1.8 weeks
E. 6.7 weeks

A department store buys a case of pencils for $25.00
and sells them at a rate of 3 for 20¢. If there are 1000
pencils in a case, the profit is approximately what
percentage of the cost?
A. 60%
B. 83.3%
C. 120%
D. 166.7% abswer
E. 216.2%

 

[PooyaH]

3. 36 week.workers to lay 1000ft, thus

it takes 43.2 week.workers to do 1200 ft.

43.2 / 8 workers = 5.4 weeks

 

[PooyaH]

2. let x be the listing price and convert the info into math, thus
.8x = 120 + .5x
x = 400

 

[PooyaH]

4.you can sell 333 stacks of 3 pencils which come out to 333 x .2 = $66.60, now you have one pencil left. The price of one pencil would be $.025 so your total earnings would be $66.625. thus,

your profit percentage would be:

(66.625 - 25) / 25 = 1.667 x 100 = 166.7%

 

[Sublimation]

Hi guys, I'm struggling with these word problems if someone can show a simple/quick way to do them, for those who took the test, were these the type of problems you saw on the real thing?


In May of 1965, a father's age was three times the sum
of the ages of his two sons. In May of 1975, the
father's age was 10 years greater than the sum of his
sons' ages. If the difference between the sons' ages is
four years, how much older is the father than his older
son?
A. 23 years answer
B. 13 years
C. 33 years
D. 27 years
E. 40 years


A dining room table is selling at a 20% discount,
which is $120 more than 1/2 the list price. What is the
list price of the table?
A. $240
B. $400 answer
C. $200
D. $360
E. $300



It takes 6 workers 6 weeks to lay 1000 feet of pipe.
How long will it take 8 workers to lay 400 yards of
pipe?
A. 5.4 weeks answer
B. 3.75 weeks
C. 3.2 weeks
D. 1.8 weeks
E. 6.7 weeks

A department store buys a case of pencils for $25.00
and sells them at a rate of 3 for 20¢. If there are 1000
pencils in a case, the profit is approximately what
percentage of the cost?
A. 60%
B. 83.3%
C. 120%
D. 166.7% abswer
E. 216.2%

I was gonna do the 2nd and 3rd lol but someone beat me to it. ok for
4. Do it this way. If you sell a box at 3 for .2. (1000/3)X(.2)=66.something then subtract 25 dollars ( the cost of the box) and you get the profit, then divide the 25. you should have somethin like 42 i think and divide by 25 and it should give u 1.68 multiply by 100 and you get D or something close to it lol. u see, the think is when u get problems with answer choices with such large differences, you can round and it just makes the calculations easier.

im trying to think of a proper mathmatical way to do the first one. i did the first one by working backwards. but let me see if i can throw something together.

 

[Streetwolf]

In May of 1965, a father's age was three times the sum
of the ages of his two sons. In May of 1975, the
father's age was 10 years greater than the sum of his
sons' ages. If the difference between the sons' ages is
four years, how much older is the father than his older
son?
A. 23 years answer
B. 13 years
C. 33 years
D. 27 years
E. 40 years

===

In 1965: f = 3(x + y) where x and y are the sons' ages and f is the father's age.

In 1975: (f + 10) = 10 + ([x + 10] + [y + 10]) <-- remember all ages are 10 more than they were in 1965.

So the second problem becomes f = x + y + 20. I would write it as f - 20 = x + y.

With that I can replace the x + y in the first equation:

f = 3(f - 20)
f = 3f - 60
2f = 60
f = 30

The difference between the ages of the sons is 4 years. This means x - y = 4, or x = y + 4.

f = 3(x + y)
30 = 3(x + y)
10 = x + y
10 = (y + 4) + y
10 = 2y + 4
6 = 2y
y = 3
x = 7

So the older son is 7 which means the father is 23 years older.

 

[PooyaH]

Hey sorry I had to jump off the pc before doing the first problem. Streetwolf is correct as usual.

If you get confused by the (x + y), I was gonna do it this way:

let the sum of the son's ages = x, then

f = 3x
f + 10 = 10 + (20 + x)
f = 20 + x, thus,

20 + x = 3x
x = 10 (therefore the age of the father = 30)

we know the age difference is 4 years; so, son(I) = son(II) - 4, and also son(I) + son(II) = 10, thus,
[son(II) -4] + son(II) = 10, and son(II) = 7

So the father's age difference is 30 - 7 = 23 yrs

 

[kov82]

hey thanks for the reply guys, but I didn't understand how you got the 43.2 weeks for 8 workers, I only knew to say that it takes one worker 36 weeks to lay 1000 feet, I converted from yards to feet, but got stuck


for the list price problem, because of the way I was interpreting the question I kept trying to put two variables, one for the sale price one for the list price .8y= 120 + .5x and now it makes sense, wow that was stupid of me


and its funny how streetwolf can even guess where someone would make a mistake, you had an arrow pointing to exactly what I was doing wrong again because of the way I was reading the problem I simply had said F +10 = 10 + (3 (x+y)) I was actually wrong about two things there, the first equation "3" should not have had anything to do with the second and I forgot to add the 10's to each age, it looks sooooo much simpler now! thanks

 

[PooyaH]

hey thanks for the reply guys, but I didn't understand how you got the 43.2 weeks for 8 workers, I only knew to say that it takes one worker 36 weeks to lay 1000 feet, I converted from yards to feet, but got stuck


for the list price problem, because of the way I was interpreting the question I kept trying to put two variables, one for the sale price one for the list price .8y= 120 + .5x and now it makes sense, wow that was stupid of me


and its funny how streetwolf can even guess where someone would make a mistake, you had an arrow pointing to exactly what I was doing wrong again because of the way I was reading the problem I simply had said F +10 = 10 + (3 (x+y)) I was actually wrong about two things there, the first equation "3" should not have had anything to do with the second and I forgot to add the 10's to each age, it looks sooooo much simpler now! thanks, did anyone get the dining table one?

You use "week.workers" as the unit to solve problems like this.
so we said that it takes 36 week.workers to lay 1000ft, now it would take 43.2 week.workers to lay 1200ft!!! (36/1000 = x/1200 and x = 43.2)

Now, we have 8 workers instead of 6, so 43.2 week.workers / 8 workers = 5.4 weeks!!! Hope it make sense.